This is called a linear system of equations.

这被称为线性方程组。

Or, we could just say it's the solution to this system of equations.

或者，我们可以说它是这个方程组的解。

That's the whole point of a linear system of equations.

这就是线性方程组的意义所在。

There are simply too many variables for this system of equations to be untangled into a general solution.

对于这个方程组来说，变量太多了，无法分解成一个通用的解决方案。

So that's a very high level overview of how to think about linear systems of equations.

这就是如何思考线性方程组的一个非常高水平的概述。

So if we find the m and the b values that satisfy the system of equations, we have minimized the squared error.

所以如果我们找到满足方程组的 m 和 b 值，我们就已经最小化了平方误差。

So the set appear will be some linear system of equations, say, with two unknowns, X and Y, and two equations.

所以集合是一个线性方程组 有两个未知数 X和Y 有两个方程。

But when the determinant is zero, and the transformation associated with the system of equations squishes space into a smaller dimension.

但当行列式为零时 与方程组相关的变换将空间压缩到更小的维度。

The relevant background here is understanding determinance, little bit of dot products, and of course, linear systems of equations.

相关的背景知识是理解行列式 一点点积 当然还有线性方程组。

When I say system of equations, I mean you have a list of variables, things you don't know, and a list of equations relating them.

当我说方程组时 我的意思是你有一个变量列表 你不知道的东西 还有一个与它们相关的方程列表。

It's the space of all vectors that become no in the sense that they land on the zero in terms of the linear system of equations.

它是所有向量组成的空间它们在线性方程组中落在0点上。

But 1st, I should say up front that this creamer's rule is not actually the best way for computing solutions to linear systems of equations.

但首先 我要提前说一下 这个奶油法则实际上并不是计算线性方程组解的最佳方法。

Next up, I'll be relating the idea of linear transformations covered so far to one of the areas where linear algebra is most useful linear systems of equations.

接下来 我将把迄今为止所涉及的线性变换的思想与线性代数最有用的线性方程组的一个领域联系起来。

But one of the main reasons that linear algebra is more broadly applicable and required for just about any technical discipline is that it lets us solve certain systems of equations.

但线性代数更广泛地适用于几乎任何技术学科的主要原因之一是它让我们求解某些方程组。

The typical way to organize this sort of special system of equations is to throw all the variables on the left and put any lingering constance on the right.

组织这种特殊方程组的典型方法是把所有的变量放在左边 而把任何残留的常量放在右边。

Again, the system of equations can be translated to the geometric interpretation, where you have some transformation A and some vector V, and you're looking for the vector X that lands on V.

同样 这个方程组可以转化为几何解释 你有一个变换A和一个向量V 你在寻找向量X落在V上。

Most important here is that you know how to think about matrices as linear transformations, but you also need to be comfortable with things like determinants, linear systems of equations and change of basis.

这里最重要的是你知道如何把矩阵看作线性变换 但你也需要熟悉行列式 线性方程组和基底变换。